Obsidian didn't manage to materialize a Khronos working group, so it's not moving forward. Apple instead went with the W3C to form the GPUWeb group, based on their work on WebGPU. The Obsidian folks at Mozilla have decided to follow this path instead, see here:
https://github.com/KhronosGroup/WebGLNext-Proposals/pull/11#...
However, there's no real writeup of what the API will end up remotely looking like right now, so it's too early to speculate. WebGPU's original prototype used Metal's shading language for instance (since the prototype came from WebKit), but any real standard probably will probably change things up.
I believe the webgpu-servo folks have, in the mean time, begun working on lower level components/libraries to target Vulkan/DX12/Metal, for use by systems like WebGPU. Sort of like ANGLE by the Chrome team, but for newer GFX APIs.
TL;DR absolutely nothing is fleshed out at all yet and it seems plenty will probably change